Question

What are the domain and range of the function f(x)= 3^x + 5?

Answer 1

domain is the numbers you can use for x
range is the numbers you get from inputing the domain for x


we don't see any restrictions (like division by 0 or square roots of a negative)
so domain is all real numbers

alright

so if we try x=-infinity, we get that 3^-ifnintiy is baseiclaly 0
so f(-infinity)≈5
if we try x=infinity, we get f(intinify)=infinity


so domain is from -∞ to ∞ and range is from 5 to ∞

2nd one

domain: (-∞,∞) range: (5,∞)

Answer 2

Domain: (-∞,∞)

Range: (5,∞)

Option 2 is correct.

Explanation:

Given:
`f(x)=3^x+5`

It is an exponential function with base 3.

`y=ab^x+c`

Domain: It is input value of x for which function defined.

All real number.

Range: It is output value of y for all defined value of x.

(c,∞)

For given function
`f(x)=3^x+5`

As we know exponential function defined for all real value of x.

Thus, Domain: All real number

Domain: (-∞,∞)

Horizontal asymptote, y=5 . Range is either above asymptote or below asymptote.

If coefficient of parent function is positive then above else below.

Here initial value is 3 which is positive.

Thus, Range: All real number greater than 5

Range: (5,∞)

Hence, The domain is (-∞,∞) and range is (5,∞)